Přístupnostní navigace
E-přihláška
Vyhledávání Vyhledat Zavřít
Detail publikace
CHEN, S. RADULESCU, V. TANG, X.
Originální název
Multiple normalized solutions for the planar Schrödinger–Poisson system with critical exponential growth
Typ
článek v časopise ve Web of Science, Jimp
Jazyk
angličtina
Originální abstrakt
The paper deals with the existence of normalized solutions for the following Schr & ouml;dinger-Poisson system with -constraint: { -Delta u+lambda u+mu(log||& lowast;u2)u=(e(u2-)1-u2)u,x is an element of R-2, integral R(2)u(2)dx=c, where mu>0,lambda is an element of R , will arise as a Lagrange multiplier and the nonlinearity enjoys critical exponential growth of Trudinger-Moser type. By specifying explicit conditions on the energy level c, we detect a geometry of local minimum and a minimax structure for the corresponding energy functional, and prove the existence of two solutions, one being a local minimizer and one of mountain-pass type. In particular, to catch a second solution of mountain-pass type, some sharp estimates of energy levels are proposed, suggesting a new threshold of compactness in the -constraint. Our study extends and complements the results of Cingolani-Jeanjean (SIAM J Math Anal 51(4): 3533-3568, 2019) dealing with the power nonlinearity a|u|p-2uin the case ofa>0andp>4, in the case of and , which seems to be the first contribution in the context of normalized solutions. Our model presents some new difficulties due to the intricate interplay between a logarithmic convolution potential and a nonlinear term of critical exponential type and requires a novel analysis and the implementation of new ideas, especially in the compactness argument. We believe that our approach will open the door to the study of other -constrained problems with critical exponential growth, and the new underlying ideas are of future development and applicability.
Klíčová slova
Critical exponential growth; Logarithmic convolution potential; Normalized solution; Planar Schrödinger–Poisson system; Trudinger–Moser inequality
Autoři
CHEN, S.; RADULESCU, V.; TANG, X.
Vydáno
16. 2. 2024
Nakladatel
Springer Nature
ISSN
0025-5874
Periodikum
MATHEMATISCHE ZEITSCHRIFT
Ročník
306
Číslo
2
Stát
Spolková republika Německo
Strany od
1
Strany do
32
Strany počet
URL
https://link.springer.com/article/10.1007/s00209-024-03432-9
Plný text v Digitální knihovně
http://hdl.handle.net/11012/245504
BibTex
@article{BUT188260, author="Sitong {Chen} and Vicentiu {Radulescu} and Xianhua {Tang}", title="Multiple normalized solutions for the planar Schrödinger–Poisson system with critical exponential growth", journal="MATHEMATISCHE ZEITSCHRIFT", year="2024", volume="306", number="2", pages="32", doi="10.1007/s00209-024-03432-9", issn="0025-5874", url="https://link.springer.com/article/10.1007/s00209-024-03432-9" }